Abstract:
We present formulas that simplify finding the solutions of the Poisson equation, the inhomogeneous polyharmonic equation, and the inhomogeneous Helmholtz equation in the case of a polynomial right-hand side. They are based on the representation of an analytic function by harmonic functions. The resulting formulas remain valid for some analytic right-hand sides for which the corresponding operator series converge. © Pleiades Publishing, Ltd., 2010.